height of a pyramid

Question

If the volume of a square pyramid is 144cm³, and if the ratio of the side lenghth of the base to the height is 1:2, what is the height of the pyramid?

Answer 1

Hi,

As you know the volume is:

V = 1/3 a^2 h that a = length of side and h = height

The ratio of the side length of the base to the height is 1:2, It means a/h = 1/2

a= h/2 then replace to the V = 1/3 a^2 h ====> 144 = 1/3 (h/2)^2 h

144 = h^3/12

h^3 = 12 *144 ====> h = 12

I hope it is useful,

Minoo

Answer 2

s = 0.5h

V = (1/3)πs²h

144 = (1/3)π(0.5h)²h

Can you solve for h and answer?